MILO SCHIELD, Augsburg College Director, W. M. Keck Statistical Literacy Project

Transcription

1 1 Statistical Literacy for All MILO SCHIELD, Augsburg College Director, W. M. Keck Statistical Literacy Project US Rep, International Statistical Literacy Project Member, International Statistical Institute President: Twin Cities Chapter, ASA Webmaster: February 24, 2012 Slides at

2 2 Statistical Literacy Statistical literacy is the ability to read and interpret summary statistics in the everyday media: in graphs, tables, statements and essays. Statistical literacy is needed by data consumers. About 40% of all US college students graduating in 2003 had non-quantitative majors. Schield (2010) in Assessment Methods in Statistical Education

3 3 Wired Magazine: Oct 2010.

4 4 Statistical Literacy: Take CARE Associations may be useful in identifying causation making a prediction, a generalization or a specification. Statistical associations may be influenced by: Context: what is (and is not) taken into account Assembly: how things are defined or measured Randomness: coincidence or margin of error Error/bias: Subject, research or sampling bias

5 1a. Association is probably not Causation.

6 1b. Association is Probably Causation Heart-Attack Survival Rate 40% 30% Survive 20% 10% 0% Jolt delayed in third of cardiac arrests Minutes to Defibrillation AP Story: 01/03/2008

7 1c. Association is possibly a sign of Causation.

8 8 Statistical Literacy Describing & Comparing Literacy is a big idea in statistical literacy Must be able to describe and compare percentages and rates presented in tables and graphs. Is the percentage of men who smoke the same as the percentage of men among smokers? No If Smoking is more likely among women than men does this mean that Smokers are more likely to be women than men? No

9 9 Small Change in Syntax; Big Change in Semantics. Edison 2009/09/26

10 10 Statistical Literacy #1: Context & Confounding Confounding is a big idea in Statistical Literacy. Controlling for a confounder can influence: the size of rates, percentages and relative risks the percentage or # of cases attributed to X whether a difference is statistically Significant Statistically-significant differences can become statistically insignificant (and vice versa). Intro statistics textbooks do NOT mention this!

11 11 Size of a statistic depends on what is taken into account State Prison Expense (1996)

12 102 February SEASON WINS vs. TOTAL PAYROLL Size of US Major a statistic League Baseball depends on what is taken into account Indians 1995 Season Wins 92 Braves Red Sox Reds 82 Yankees Rangers 72 Mets Padres Orioles Expos Marlins 62 Pirates Tigers Twins BlueJays Total Payroll ($Millions)

13 13 US SAT-VERBAL SCORES

14 14 Patient Death Rates City hospital has a higher death rate than Rural. After controlling for patient condition (compare within a given column), City hospital has a lower death rate than Rural.

15 15 Death Rates per 10,000 Auto Accidents People in auto accidents are less likely to die if their car has an air bag. After controlling for the use of a seat belt (compare in a column), airbags make almost no difference in survival compared to seat belts (compare in a row)

16 16 Assembly: Making small things big 7 nanograms per gram = 7 parts in a billion 4/2010 National Geographic

17 17 Hyatt: Close to the US Capital.

18 18 Randomness: Coincidence.

19 19 Randomness: Coincidence?.

20 20 Seeing Coincidence.

21 21 Flip 8 sets of 3 coins each [24 flips]; A run of three heads is expected Chance of 3 heads: one chance in eight.

22 22 Run of at least three heads: Expected in 10 flips of fair coin. Key is Overlap

23 23 Error/Bias Suppose that men make a third more income than women for the same job. How much of this difference is due to bias? Lying or reaching by men. Rounding up. Including anticipated bonus/raise. Conservatism by women. Rounding down. Quoting regular pay or even take-home pay.

24 24 Error/Bias A recent survey shows that most Republicans surveyed prefer Obama as President. Question: Who would you prefer as President? Barack Obama The captain of the Italian linear that crashed Charlie Sheehan Lady Gaga

25 Conclusion #1 Most students are statistically illiterate They don t believe that taking into account a related factor can change an association. They can t see why coincidences are common. They can t read tables or graphs. They can t describe and compare rates and percentages. They can t think hypothetically about what might have influenced an association. They don t see how definitions affect numbers.

26 Conclusion #2 Graduates in non-quantitative majors are most likely to be the journalists, policy makers and politicians who influence decisions on funding for science, engineering and math. The less value they see in STEM, the harder it is to get their support.

27 27 Recommendation Find Way to Support Mathematics departments should find ways to support courses and programs involving quantitative or statistical literacy as a form of math-statistics appreciation. Increased appreciation should be first; understanding principles taught in upperlevel math-stat courses should be second.

28 Importance of Statistical Literacy I ve been increasingly impressed by how important statistical literacy has become for all of us around the globe. Statistical literacy has risen to the top of my advocacy list, right alongside numeracy, and perhaps even ahead of algebra for all. J. Michael Shaughnessy, NCTM President

29 29 Wired Magazine: Oct 2010.

30 30 References Schield (1999). Simpson's Paradox and Cornfield's Conditions. Schield, Milo (2006). Presenting Confounding and Standardization Graphically. STATS Magazine, See Schield, Milo (2012). Coincidences. MAA Boston. See